1. Hi, mathematicians. In the following link, there are Euler's articles and books coded as E1, E2, E3,.... I wonder in which article he introduces his special number which we now know as the number "e".

http://www.math.dartmouth.edu/~euler/  2.

3. This wouldn't be a reading assignment for a class would it?  4. No Numsgil. I am interested in physics and mathematics history. I'm tryin to understand for example how the classical mechanics has developed in the history from Galileo to Newton, Lagrange, Hamilton... So I wonder the number "e". Because there are too many articles by the mathematician Euler, I want the mathematicians to help me where Euler first used it.  5. Well, Euler wrote like a madman (meaning he was prolific, not crazy :P)

But IIRC, he first used the number when he was working on logarithms.  6. I searched the logarithms topics in the cite I linked and found it in the E168 article in 1747. I suppose that it was the firts time he used the number, was it? If I can not reply to your post excuse me! because I will go to bed. here is the night in İstanbul :-D
see you  7. http://en.wikipedia.org/wiki/E_(mathematical_constant)

The first known use of the constant, represented by the letter b, was in correspondence from Gottfried Leibniz to Christiaan Huygens in 1690 and 1691. Leonhard Euler started to use the letter e for the constant in 1727, and the first use of e in a publication was Euler's Mechanica (1736).  8. thank you very much Harold14370 for your inform. I did not know that it's history go back to 1690.  9. I do wonder, what is the use of 'e'? or rather, what makes it so special?  10. It's special because .  11. Originally Posted by MagiMaster
It's special because .
Absopositively correct.

What is important is the exponential function, not the number e. The exponential function extends to lots of other useful things. For instance makes perfect sense if x is a matrix, or even a bounded operator on a Banach space. That turns out to be important in systems of ordinary differential equations with constant coefficients. It extends to complex numbers and an important special case is Euler's formula for x real.

How do you do that ? It is easy. Just start with the power series for and let x be a matrix or an operator. The series converges absolutely.  Bookmarks
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